Greengage, the virgin mated or not, will produce drones from her own genetic background eg queen sex alleles = A/C her drones will be A and C, when she mates with drone D her female offspring will be A/D and C/D
hope that makes sense
if your A/C queen was fertalized with drones from the same hive she was reared from ie A and C then the worker prodgeny would be A/A, A/C, C/C, and C/A. In this case there would be 50% inbreeding and the hive would never survive without a lot of help. This is of course simplistic as there are many different drones available to mate with your queen ie B,D,E,F,G etc...
should of added that females with same sex alleles eg C/C are not viable as the bees normally destroy these eggs
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